Solve the problem.
-Jarrod has a choice between two job offers. Job A has an annual starting salary of $\$ 20,000$ with guaranteed annual raises of $\$ 700$ for the next four years, while Job B has an annual starting salary of $\$ 19,000$ with guaranteed annual raises of $\$ 2600$ for the next four years. Compare the fifth partial sums for each sequence to determine which job would pay Jarrod more over the next 5 years.
A) Job B pays $\$ 22,500$ more over the next 5 years.
B) Job B pays $\$ 14,000$ more over the next 5 years.
C) Job A pays $\$ 1000$ more over the next 5 years.
D) Job A pays $\$ 7400$ more over the next 5 years.

Question

Quizplus · Accepted Answer

To compare the total pay over 5 years for each job, we calculate the fifth partial sums for each sequence. For Job A, the total pay over 5 years is $20,000 + (20,000 + 700) + (20,000 + 2(700)) + (20,000 + 3(700)) + (20,000 + 4(700)) = 20,000 \times 5 + 700(1+2+3+4) = 100,000 + 700 \times 10 = 107,000$. For Job B, the total pay over 5 years is $19,000 + (19,000 + 2600) + (19,000 + 2(2600)) + (19,000 + 3(2600)) + (19,000 + 4(2600)) = 19,000 \times 5 + 2600(1+2+3+4) = 95,000 + 2600 \times 10 = 121,000$. Subtracting Job A's total from Job B's total gives $121,000 - 107,000 = 14,000$, so Job B pays $14,000 more over the next 5 years.

Solve the Problem $20,000\$ 20,000$20,000 With Guaranteed Annual Raises Of $700\$ 700$700

Solve the Problem $\$ 20,000$ With Guaranteed Annual Raises Of $\$ 700$